Since the coefficients in the regression represent key parameters such as elasticities and cross-elasticities of demand, it is important that we test their statistical significance.

The t-test is used for this purpose. For each coefficient, it tests that the coefficient differs significantly from zero value.

Consider the regression model: $$ y = b_0+b_1 x_1+b_2 x_2+b_3 x_3 \,…$$

For the coefficient b_{1}, in the above equation:

Null hypothesis H0: b_{1} = 0

Alternative hypothesis HA: b_{1} <> 0

Relevant test statistic is t = b_{1} /σb_{1}, where σb_{1} is the
standard error of b_{1}.

Relevant distribution is the t-distribution, with degrees of freedom = n − (k + 1). Where k is the number of explanatory variables, and n is sample size.

Similar tests are run for b_{2}, b_{3} … to determine the individual
significance of X_{2} and X_{3} in the model.

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